To convert the base-6 number $45113_6$ to a base-10 (decimal) number, follow these steps:

Step 1: Write the base-6 number in expanded form.

Each digit represents a power of 6, starting from the rightmost digit (which is $6^0$).

$45113_6 = 4 \cdot 6^4 + 5 \cdot 6^3 + 1 \cdot 6^2 + 1 \cdot 6^1 + 3 \cdot 6^0$

Step 2: Calculate the powers of 6.

$6^0 = 1,\quad 6^1 = 6,\quad 6^2 = 36,\quad 6^3 = 216,\quad 6^4 = 1296$

Step 3: Multiply the digits by the powers of 6 and sum the results.

$45113_6 = (4 \cdot 1296) + (5 \cdot 216) + (1 \cdot 36) + (1 \cdot 6) + (3 \cdot 1)$ $= 5184 + 1080 + 36 + 6 + 3$ $= 6309$

Thus, $45113_6$ in base-10 is: $45113_6 = 6309_{10}$

Final Answer:

$(45113)_6 = (6309)_{10}$

Would you like further details or explanations?

Here are 5 related questions to consider:

1. How would you convert a base-10 number to base-6?
2. Can you explain why each position in base-6 is a power of 6?
3. How would this process change for other bases, like base-8 or base-12?
4. What are some practical applications of base conversions?
5. How would you convert fractional numbers from base-6 to base-10?

Tip: Always double-check the powers and multiplications when converting between bases to avoid small errors!